Estimate Std. Error t value Pr(>Itl) (Intercept) 4.6519 43.7118 0 . 106 0. 9158 MRI 1 . 1766 0. 4806 2 .448 0. 0194 * Signif. codes: 0 '*0.001 '*' 0.01 '' 0.05 ".' 0.1 ' ' 1 Residual standard error: 21.21 on 36 degrees of freedom Multiple R-squared: 0. 1427 , Adjusted R-squared: 0. 1189 F-statistic: 5.994 on 1 and 36 DF, p-value: 0.01935 (a) From the above results, compute the variance inflation factor for MRI. Please show all the intermediate steps. (b) From the above results, compute the value of the F-statistic for testing in the first model that the regression coefficients for both Height and Weight are equal to zero. Based on the computed value, report the P-value of the test.4. People were interested in understanding whether a person's brain size and body size are predictive of his/her intelligence. Data on the intelligence based on the performance IQ scores (PIQ), brain size based on MRI scans (MRI), and body size measured by height in inches (Height) and weight in pounds (Weight) were collected from 38 college students. Amy performed two regression analyses on this data set. The R output of the first analysis is the following: > piq . multi . fit summary (piq-multi . fit) Call : Im (formula = PIQ * MRI + Height + Weight, data = piq) Coefficients: Estimate Std. Error t value Pr(>It!) (Intercept) 1. 114e+02 6.297e+01 1.768 0.085979 MRI 2. 060e+00 5.634e-01 3. 657 0.000856 * * * Height -2.732e+00 1.229e+00 -2.222 0.033034 * Weight 5.599e-04 1.971e-01 0. 003 0.997750 Signif. codes: 0 '* **' 0.001 '**' 0.01 '*' 0.05 " .' 0.1 ' ' 1 Residual standard error: 19.79 on 34 degrees of freedom Multiple R-squared: 0.2949, Adjusted R-squared: 0.2327 F-statistic: 4.741 on 3 and 34 DF, p-value: 0.007215 The R output of the second analysis is: > piq . mri . fit summary (piq . mri . fit) Call : Im (formula = PIQ ~ MRI, data = piq) Coefficients